For he finds fault with them when he says: “Behold, the days are coming, declares the Lord, when I will establish a new covenant with the house of Israel and with the house of Judah,
8. Behold, the days come, etc. (Jeremiah 31:31-34.) The Prophet speaks of future time; he arraigns the people of perfidy, because they continued not faithful after having received the Law. The Law, then, was the covenant which was broken, as God complains, by the people. To remedy this evil, he promised a new and a different covenant, the fulfillment of which prophecy was the abrogation of the old covenant.
In this part of the chapter, the apostle illustrates and confirms the superior excellency of the priesthood of Christ above that of Aaron, from the excellency of that covenant, or that dispensation of the covenant of grace, of which Christ was the Mediator (Heb 8:6): his ministry is more excellent, by how much he is the Mediator of a better covenant.
Commenting on Hebrews 8:6-13
For finding fault with them,.... Both with the covenant, which had its faults, and with the people who continued not in it, and were therefore disregarded by the Lord, Heb 8:9 he saith, behold, the days come (saith the Lord) when I will make a new covenant with the house of Israel, and with the house of Judah; the words are cited from Jer 31:31...